Hmm...
Option 1 - redefine the World Series. Instead of being between AL and NL, it works more like the Little League World Series or the World Cup, with regional or national teams winning meeting. For this, you'd need baseball to be more popular abroad, a more regional focus to baseball in general, and (of course) enough talent for Britain to actually win. I'm not sure what would be needed internationally, but if the Pacific Coastal League had been able to establish itself as a third major league, that could've helped promote a more regional structure for the Major Leagues. Also, it would be immensely useful for Federal Baseball Club v. National League to go the other way, preventing the antitrust exemption for the AL and NL that gave them such power over the minor leagues.
Option 2 - get a team in London. For this, you'd need more interest in baseball in Britain itself - but there's the problem of how you'd justify having a single team in London, one that has far more arduous road trips than anyone else. So you'd need other teams - perhaps 4-5 teams total, enough to have an entire division. Teams could be in London, Glasgow, Manchester, Dublin and maybe Reykjavik or Liverpool? How do you get 4-5 more teams into MLB? You'd need to show interest in the sport beforehand, and at the right time - when transatlantic travel is sufficiently easy and when MLB is prospering. Probably the best time for such an expansion would be in the 1990s, when four teams were added historically; unfortunately, they were added two at a time, not four all at once, and were responses to the growth of Florida and the Mountain West as markets for American products.
So, there's a start.